The term independent of x in the expansion of (x3+(2/x2))15 is

Question

The term independent of x in the expansion of (x3+(2/x2))15 is (A) 7 text th  (B) 8 text th  (C) 9 text th  (D) 10 text th

Tardigrade Admin · Accepted Answer

T r +1= 15 C r ⋅( x 3)15- r ((2/ x 2)) r = 15 C r x 45-3 r ⋅ 2 r ⋅ x -2 r = 15 C r x 45-5 r ⋅ 2 r Term independent of ' x ' ⇒ 45-5 r =0 ⇒ r =9 text Term = T 9+1= T 10

Q. The term independent of $x$ in the expansion of $(x^{3} + \frac{2}{x ^{2}})^{15}$ is

$7^{th}$

$8^{th}$

$9^{th}$

$1 0^{th}$

$T_{r + 1} =^{15} C_{r} \cdot (x^{3})^{15 - r} (\frac{2}{x ^{2}})^{r}$
$=^{15} C_{r} x^{45 - 3 r} \cdot 2^{r} \cdot x^{- 2 r}$
$=^{15} C_{r} x^{45 - 5 r} \cdot 2^{r}$
Term independent of ' $x$ ' $\Rightarrow 45 - 5 r = 0 \Rightarrow r = 9$
$Term = T_{9 + 1} = T_{10}$

Q. The term independent of x in the expansion of (x3+x22​)15 is

7th

8th

9th

10th